ABC News/Andy Field(WASHINGTON) -- The Supreme Court takes up oral arguments on Tuesday in a controversial case that could set a precedent for whether businesses are allowed to turn away customers based on religious beliefs.

The case is tied to a baker in Colorado, who says he has the right under the First Amendment to refuse to bake a wedding cake for a same-sex couple. The incident in question took place in 2012, when a gay couple visited Masterpiece Cakes in Lakewood, Colorado and asked for a custom cake -- a request the owner declined.

Jack Phillips, the owner of Masterpiece Cakes, in court documents says he "gladly serves people from all walks of life, including individuals of all races, faiths, and sexual orientations. But he cannot design custom cakes that express ideas or celebrate events at odds with his religious beliefs."

Colorado courts have sided with the couple, David Mullins and Charlie Craig, who say they were "denied the same full and equal service that would've been provided to any other customer."

Supreme Court expert Kate Shaw answers our questions about the case, and what it could mean for the future.

What is the case about?

This case involves a Colorado baker’s denial of service to a same-sex couple. The case began when David Mullins and Charlie Craig, a couple planning their wedding, made an appointment to discuss a custom wedding cake with Jack Phillips, the proprietor of Masterpiece Cakeshop. When Phillips learned that Mullins and Craig were a same-sex couple, he indicated that he did not design cakes for gay weddings, but that he would be willing to sell them other baked goods. Craig and Mullins left the bakery.

Colorado has a state law that prohibits discrimination on the basis of sexual orientation, and the couple filed a complaint with the Colorado Civil Rights Division, which agreed that Phillips’ conduct violated state law. The Colorado state courts agreed.

Phillips has appealed all the way to the Supreme Court, arguing the Colorado law violates the Constitution, both by requiring him to violate his religious beliefs and by compelling him to bake a particular cake -- which he describes as a form of artistic expression -- for an event not of his choosing.

Are there any other players in this case?

Well, one very important player is the Trump Justice Department, which has filed a brief supporting Phillips. There are also close to 100 additional amicus briefs in the case -- a strong indication of the intense public interest in the case. People have been camping outside the Supreme Court since Friday in the hopes of getting to see the arguments in person.

What are the possible results in this case?

First, Phillips could prevail in his argument that a state law requiring him to bake cakes for couples like Mullins and Craig would either constitute “compelled speech” in violation of the First Amendment, or would violate his religious exercise rights under the First Amendment’s Free Exercise Clause.

Or, Mullins and Craig, who are joined by the Colorado Civil Rights Commission, could persuade the justices that neither the speech nor the religion guarantees of the First Amendment permit Phillips to discriminate on the basis of sexual orientation in his commercial activity.

How are the justices expected to rule?

This is an extremely difficult case to predict. It will almost certainly come down to Associate Justice Anthony Kennedy, and his previous opinions point in a few different directions. He’s the author of the Supreme Court’s most important gay rights decisions -- most notable the court’s recent decision in Obergefell v. Hodges, which opened up marriage to same-sex couples.

But he also has an extremely expansive conception of the First Amendment. Those two commitments are in genuine conflict, and it’s anyone’s guess which one will have to yield.

We’ll likely have a better sense after oral arguments, but until the opinion is out, which I’d guess won’t be until June 2018, it’s anyone’s guess.